Inclusion Criteria:

          -  Arms 1 & 2: Histologically or cytologically confirmed advanced/metastatic solid tumor
             by pathology report and has received or been intolerant to all treatment known to
             confer clinical benefit

          -  Arm 3: Histologically or cytologically confirmed diagnosis of stage IV (M1a or M1b per
             current American Joint Committee on Cancer criteria) nonsquamous NSCLC

          -  Arm 4: Triple-negative breast cancer (TNBC) that is locally recurrent, inoperable, not
             previously treated with chemotherapy, and which cannot be treated with curative intent
             OR metastatic disease not previously treated with chemotherapy

          -  Measureable disease by RECIST 1.1. as assessed by the local site
             investigator/radiologist. Target lesions situated in a previously irradiated area are
             considered measurable if progression has been demonstrated in such lesions

          -  Adequate organ function

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          -  Male participants must agree to use adequate contraception during the treatment period
             and for at least 120 days after the last dose of MK-5890 or pembrolizumab OR 180 days
             after the last dose of chemotherapeutic agents and refrain from donating sperm during
             this period

          -  Female participants must not be pregnant or breastfeeding and agree to follow use
             adequate contraception during the treatment period and for at least 120 days after the
             last dose of MK-5890 or pembrolizumab OR 180 days after the last dose of
             chemotherapeutic agents

          -  Submit an evaluable baseline tumor sample for analysis (either a newly obtained or
             archival tumor sample)

        Exclusion Criteria:

          -  History of a second malignancy, unless potentially curative treatment has been
             completed with no evidence of malignancy for 2 years

          -  Clinically active central nervous system metastases and/or carcinomatous meningitis

          -  Has had a severe hypersensitivity reaction to treatment with a monoclonal antibody
             (mAb) and/or other components of the study treatment

          -  Active infection requiring systemic treatment

          -  History of interstitial lung disease

          -  History of (noninfectious) pneumonitis that required steroids or current pneumonitis

          -  Symptomatic ascites or pleural effusion

          -  Previously had a stem cell or bone marrow transplant

          -  Previously had a solid organ transplant

          -  Active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive
             drugs) except vitiligo or resolved childhood asthma/atopy

          -  Known human immunodeficiency virus (HIV) and/or active and acute Hepatitis B or C
             infections

          -  Not fully recovered from any effects of major surgery without significant detectable
             infection

          -  Pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the study

          -  Had chemotherapy, definitive radiation, or biological cancer therapy within 4 weeks (2
             weeks for palliative radiation) before the first dose of study treatment, or has not
             recovered to Grade ≤1 or better from any AEs that were due to cancer therapeutics
             administered more than 4 weeks earlier

          -  Expected to require any other form of antineoplastic therapy while participating in
             this study

          -  On chronic systemic steroid therapy in excess of replacement doses (e.g., exceeding 10
             mg/day of prednisone equivalent), or on any other form of immunosuppressive medication

          -  Regular user (including "recreational use") of any illicit drugs at the time of
             signing informed consent, or has a recent history (within the last year) of substance
             abuse (including alcohol), as determined by the treating investigator. Participants
             who use cannabis for medicinal purposes or to treat specific symptoms will not be
             excluded unless it is being abused in the opinion of the treating investigator

          -  Received a live-virus vaccine within 28 days before the first dose of study treatment

          -  Currently participating and receiving study treatment in a study of an investigational
             agent or has participated and received study treatment in a study of an
             investigational agent or has used an investigational device within 28 days before the
             first dose of study treatment

        Additional Exclusion Criteria for Participants in Arm 3:

          -  Has received radiation therapy to the lung that is >30 Gray (Gy) within 6 months
             before the first dose of study treatment

          -  Is unable to interrupt aspirin or other nonsteroidal anti-inflammatory drugs (NSAIDs),
             other than an aspirin dose ≤1.3 g per day, for a 5-day period (8-day period for
             long-acting agents, such as piroxicam).

          -  Is unable or unwilling to take folic acid or vitamin B12 supplementation

        Additional Exclusion Criteria for Participants in Arm 4:

          -  Has a known history of hypersensitivity or allergy to nab-paclitaxel or any of its
             components

          -  Has neuropathy ≥Grade 2

          -  Has a history of class II-IV congestive heart failure or myocardial infarction within
             6 months of randomization

          -  Has received previous treatment with immune checkpoint inhibitor(s) (eg, Programmed
             Cell Death Receptor 1 (PD-1)/PD-L1)